;     Date: Mon, 12 Mar 2012 08:21:54 -0400
;     From: Jim Muth <jimmuth@earthlink.net>
;  Subject: [Fractint] FOTD 11-03-12 (No Discontinuities [5])
;       Id: <1.5.4.16.20120312072406.2b4770b6@earthlink.net>
; ---------
; 
; FOTD -- March 11, 2012 (5)
; 
; Fractal visionaries and enthusiasts:
; 
; Today's fractal is an outzoom of yesterday's image, which lies 
; in the fractal debris on the northeast side of today's minibrot.
; 
; Today's FOTD is a close-up of a minibrot halfway through the 
; process of morphing from quadratic to cubic, and doing so 
; without discontinuities.  The iterated expression is not the 
; expected Z^(2.5)+C, it is sqr(Z)*(recip(Z^(3)+30))+C.  And since 
; no fractional exponents are involved, no discontinuities will 
; appear in the fractals it creates.
; 
; I have never understood exactly how the JulibrotMulti or similar 
; formulas work, but today's image shows a perfect minibrot of 
; order 2.5 without the frustrating broken-up bits and pieces that 
; spoil so many otherwise good fractals.
; 
; The name "No Discontinuities" simply describes the minibrot.
; 
; I could give the image a rating no higher than a 5, which 
; indicates its mathematical worth.  I put almost no effort into 
; the coloring, so the artistic worth is near zero.
; 
; The calculation time of 45 seconds is blessedly brief, but 
; viewing the finished image on one of the FOTD web sites is more 
; convenient.
; 
; The finished image, already calculated for maximum convenience, 
; is posted on the official FOTD web site at:
; 
;       <http://www.crosscanpuzzles.com/Archives.html>
; 
; The high-definition version is posted at:
; 
; <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
; 
; The original FOTD web site may be accessed at:
; 
;        <http://www.Nahee.com/FOTD/>
; 
; Lots of sunshine and much warmer temperatures arrived at Fractal 
; Central today.  The fractal cats heartily approved of the high 
; temperature of 57F 14C and showed their approval by sharing the 
; sunny shelf without quarreling.  The humans, FL and I, had an 
; everyday day, whatever that might be.
; 
; The next FOTD will be posted in 24 hours.  Until then, take 
; care, and when someone survives a tornado that destroys his town 
; and kills his friends, why does he claim to have been blessed?  
; If that person were realistic, he would think rationally.  
; Before he assumed his survival was a blessing, he would wonder 
; whether he would welcome a similar blessing next year.
; 
; 
; Jim Muth
; jimmuth@earthlink.net
; 
; 
; START PARAMETER FILE=======================================

No_Discontinuities { ; time=0:00:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=JulibrotMulti function=recip
  center-mag=-0.872575097/+29.735974572/5146/1/100/0
  params=3/30/0/0/0/0/0/0/0/0 float=y
  maxiter=1500 inside=0 periodicity=6
  colors=000UZYWaXZcX`fXchWejWhmWjoWmqVotVrvVtxVruXp\
  sYnqZlo_jm`hjafhbdfccddabe_`fYYgWWhUUiSSjQQkIJsPOl\
  VTeaYZgbSngLvkCtlEslGrlIpmKomMnmNlnPknRjnThnVgoXfo\
  Ydo_cpabpc`pe_pgZqhXqjWqlVrnTrpSrrKArKBsKCtKDtKEuK\
  FuKGvKHwKIwKJxKKzKLxKMwKNuKOtKQrKRqLSoLTnLVlLWkLXj\
  LYhL_gM`eMadMbbMdaMe_MfZOfaMgYKgVIhRGhOEiLCiHAjE8j\
  A6k70j05k59lADmFHnKLoPPpUTqZXrc`shdtmhurlvvmwzmxzm\
  yzmwzmuvmtrmrmpqhnocmnaklZjjXhiUggSefPddNbcLaaI__G\
  ZZDXXBWW8UU6ZN1TT4OZ6Id9y4ADiBJaEPVHiBEUOJF`O0mT5l\
  R9kQDjPHiOLhNPgMOeONcPMaRM_SLZUKXVKVXJTYIR_HQ`HObG\
  McFKeFJfHKdILbKMaLN_NNZOOXQPWRQUTRTURRWSQXTOZUN_UL\
  aVKbWIdXHeYFgYEhZCj_Bk`9mb7l`8l_8lZ8kY8kX8kW9kV9jU\
  9jT9jS9jR9iQAiPAiOAiNAhMAhLAhKBhJBgIBgHBgGBgFBhEEi\
  DHjDJjCMkBOlBRlATm9Wn9Yn8`o8bp7ep6gq6jr5lr4os4qt3t\
  t3vrCjpK_nSOm_DlXDkVEkTEFPFFRIETLDVNDXQCZTC`WBbZBd\
  aAfcCJZFLZHOZKQZMSYPVYRXY }

frm:JulibrotMulti  {; draws all slices of Julibrot
  pix=pixel, u=real(pix), v=imag(pix),
  a=pi*real(p2*0.0055555555555556),
  b=pi*imag(p2*0.0055555555555556),
  g=pi*real(p3*0.0055555555555556),
  d=pi*imag(p3*0.0055555555555556),
  ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
  sg=sin(g), cd=cos(d), sd=sin(d),
  p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
  q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
  r=u*sg+v*ca*sb*cg, s=v*sin(a), aa=-(real(p1)-2),
  bb=imag(p1)-0.0000000000000000001,
  c=p+flip(q)+p4, z=r+flip(s)+p5:
  z=z*z*fn1(z^(aa)+bb)+c
  |z|< 100000000 }

; END PARAMETER FILE=========================================
; 
; 
; 
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